None, one, or two
Stand at three spots near a round park. How many tangent lines can you draw from each spot?
- One circle. Point A sits inside it.
- Point B sits on the circle — 1 tangent.
- Point C sits outside — 2 tangents.
One comparison decides the count
From a spot inside the park, you can draw no tangent. From a spot on the circle, one. From a spot outside, two. Let d be the spot's distance from the centre. Let r be the radius. Compare d with r.
The rule: look at the point's distance from the centre. Less than the radius gives no tangent. Equal to the radius gives exactly one. More than the radius gives exactly two.
Point A is inside. Any line through it crosses the circle twice. So no line through A is a tangent. Point B is on the rim, the circle's edge. Only one line touches the circle at B: the tangent there. Point C is outside. Turn a line around C until it just touches the circle. That happens once on each side.
| Position | Distance vs radius | Tangents |
|---|---|---|
| Inside the circle | less | none |
| On the circle | equal | exactly one |
| Outside the circle | more | exactly two |
Compare d with r. Tap the number of tangents.
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